To obtain optimally incoherent work, it is thus expected that the battery after charging has vanishing coherence and vanishing entanglement, i.e., \(S_\Delta (T)=0\) .
Thus, incoherent quantum batteries are
promising candidates, e.g, the CS battery.
We also observe from the definitions of extractable work (REF ) and (REF ) that optimal work can be achieved when \(\rho _b(T)\)  is located in the highest energy state, which is also required that \(S_\Delta (T)=0\) .
So we can identify optimally incoherent work with optimal work.
On the other hand, to obtain optimally coherent work, it is naturally expected that \(\rho _b(T)\)  is in a maximally coherent state.
Due to the complementarity between maximal coherence and entanglement [1]}, we give priority to QBs that have no chargers and are charged by only some external fields.
Next, we will give concrete examples to achieve optimally coherent and incoherent work.
